The lengths of four sides of a trapezoid have the ratios 1: 1: 1: 2. The area is equal to 48√3. What is the perimeter of the figure? I divided the figure into two 30-60-90 triangles and a quadrilateral. Are there any isosceles trapezoid properties I need to use. Please try to find the solution.

mathleteig Nov 2, 2019

#1**+4 **

We can imagine an isosceles trapezoid with equal sides = S, a top base of S, and a bottom base of 2S

The height of the trapezoid can be found as :

√[ S^2 - [(1/2)S]^2 ] = √[(3/4)S^2]= √3 S / 2

So.....the area = (1/2)Height * (Sum of the bases).....so we have that

48√3 = (1/2) ( √3 S)/2 * (S + 2S)

48√3 = (√3S / 4) * (3S)

48 = S / 4 * (3S)

192 = 3S^2 divide both sides by 3

64 = S^2 take the positive root

8 = S

So the perimeter is S + S+ S + 2S = 3S + 2S = 5S = 5 (8) = 40 units

CPhill Nov 2, 2019